Preventing heterosexual couples from entering into civil partnerships is discriminatory and a disproportionate restriction on their right to family life, the supreme court has been told.

Opening legal argument in the test case on the future of such unions, Karon Monaghan QC said many people have well-founded reasons for not wishing to get married.

The appeal has been brought by Rebecca Steinfeld, 37, and Charles Keidan, 41, who want to enter into a legal arrangement but are banned because the Civil Partnership Act 2004 allows only same-sex couples to participate.

“They have deep-rooted and genuine ideological objections to marriage,” Monaghan explained. “I want to observe that they are not alone in holding those deep-rooted objections.”

Matrimony, she said, was “historically heteronormative and patriarchal” and the couple’s objections were not frivolous. “These are important issues, no small matters, and they are serious for my clients because they cannot marry conformable with their conscience and that should weigh very heavily indeed.”

Keidan and Steinfeld, who live in Hammersmith, west London, and have crowdfunded their legal campaign, lost earlier challenges at the high court and court of appeal – although the latter ruled that the government’s wait-and-see approach was discriminatory. “One legal regime for different-sex couples but two legal regimes for same-sex couples will ultimately be unsustainable,” it declared.

Before the hearing, Steinfeld and Keidan said: “We have met hundreds of couples like us who love each other and want a civil partnership so they can celebrate their commitment and strengthen the security of their family unit.

“All they want is the choice of marriage or a civil partnership to suit them, which is currently available only to same-sex couples. We have a new equalities minister and she should take this opportunity to look afresh at the Government’s position. It’s time for the government to stop making excuses which play with people’s lives, and give choice to all now.”

The government has said it intends to see how extending marriage to same-sex couples affects demand for civil partnerships before making a final decision.

The Conservative MP Tim Loughton, a former children’s minister, is supporting the couple. “The government should address the clear inequality within the law and bring forward appropriate legislation to make the necessary changes,” he said outside the court.

“My [private member’s bill on civil partnerships] gives the government that opportunity and I urge the new equalities minister [Penny Mordaunt] not to waste taxpayers’ money on expensive court cases and instead use my bill to extend civil partnerships.”

At the weekend, the government was reported to be considering abolishing all civil partnerships rather than extending them in order to avoid the problem of discrimination.

That suggestion prompted the gay rights charity Stonewall to condemn any attempt to end civil partnerships.

“While many have converted their civil partnership to a marriage, many thousands of same-sex couples haven’t – and don’t want to,” Paul Twocock, the organisation’s campaign director, said. “They want to maintain the integrity of the day they made their commitment to each other in a civil partnership.

“It’s not right for any government to take that away. Abolition would imply that civil partnerships are now less valued than a marriage and somehow irrelevant. Nothing could be further from the truth for those couples already in them.”